# If = (a + ib), find the values of a and b.

Given: Consider the given equation, Now, we rationalize [Here, we multiply and divide by the conjugate of 1 + i]  Using (a + b)(a – b) = (a2 – b2)   [ i2 = -1] = (-i)100

= [(-i)4]25

= (i4)25

= (1)25

[ i4 = i2 × i2 = -1 × -1 = 1]

(a + ib) = 1 + 0i

On comparing both the sides, we get

a = 1 and b = 0

hence, the value of a is 1 and b is 0

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Evaluate:

(i) (iii) .

RS Aggarwal - Mathematics